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HW1 - = BIM 108 Biomedical Signals and Control Spring 2008...

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========================================== BIM 108 Biomedical Signals and Control Spring 2008 ========================================== Homework #1 Reading Assignment : Sections 1.1 – 1.5, 3.1, 3.3 1. Show that each of these signals is equal to a sum of rectangular pulses p τ (t) and/or triangular pulses ( 1 - 2 | t |/ τ ) p τ ( t ). 2. Determine whether the following systems are linear or nonlinear. ( ) x t is an arbitrary input and ( ) y t is the zero-state response to ( ) x t . a. ( ) 2 ( ) 3 y t x t = + b. ( ), | ( ) | 1 ( ) 0, x t x t y t otherwise > = c. ( ) 4 ( ) ( ) d y t y t x t dt + = 1 2 0 -1 -2 (a) x(t) 1 2 1 2 0 -1 -2 (b) 1 3 4 -4 -3 1 2 0 -1 -2 (c) 1 2 3 1 2 0 -1 -2 (d) 1 1 2 0 (e) 1 3 4 5 ··· (repeats) t t t t t x(t) x(t) x(t) x(t)
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d. ( ) cos( ( )) y t x t = e. ( ) cos( ) ( ) y t t x t = f. ) ( ( ) t t e x y t d λ λ λ −∞ = 3. Determine whether the systems in problem 2 are causal or noncausal. 4. Determine whether the systems in problem 2 have memory or are memoryless. 5. Determine whether the systems in problem 2 are time invariant or time varying. 6. A LTI system responds to the input
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